Single-molecule stretching experiments of flexible (wormlike) chain molecules in different ensembles: Theory and a potential application of finite chain length effects to nick-counting in DNA

We propose a formalism for deriving force–elongation and elongation–force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality to the numerical evaluation of Marko and Siggia’s variational theory and considerably more precise than their interpolation formula. A comparison to numerical data suggests that our analytical finite chain length corrections achieve a comparable accuracy. As an application of our results, we discuss the possibility of inferring the time-dependent number of nicks in single-molecule stretching experiments on double-stranded DNA from the accompanying changes in the effective chain length.